Some Objections to Putnam’s “Consistency Objection”

This paper is a critical analysis of Putnam’s “consistency objection,” an objection made against a particular reading of Wittgenstein’s philosophy of mathematics. I show that Putnam’s objection presupposes a rather unlikely version of Wittgenstein’s “up-to-us-ism” and is unable to undermine a more likely anti-Platonist version. I also show that a companion argument, is unable to overturn this more sophisticated anti-Platonist version of Wittgenstein’s up-to-us-ism. Along the way I try to clarify Wittgenstein’s anti-Plalonist account of mathematics, so that others do not repeat Putnam’s mistake.